Explain the outcome of 3^4^5. In particular, what is the order of execution of the two exponentiation operations?

Explain the outcome of 3^4^5. In particular, what is the order of execution of the two exponentiation operations?
Write (5^4^3)−1 as a product of prime numbers.
The greatest common divisor of two integers a and b can be written as a linear combination (with integer coefficients k and ℓ) of a and b: gcd(a,b)=ka+ℓb.

In Sage this is achieved with the command xgcd. Look in the help page of this command to write the greatest common divisor of 12214 and 2012 as an integer linear combination of these two numbers.

Use Sage to verify your result.
What is the difference in Sage between 1/3+1/3+1/31/3+1/3+1/3 and 1.0/3+1.0/3+1.0/31.0/3+1.0/3+1.0/3? Explain.

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Expert Solution

Colby Messinger answered 2 years ago

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